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The Understanding of Particle-Wave Duality (Can it be fully understood?)

  1. Jan 22, 2010 #1

    Why would a double-slit experiment for things like bullets being fired from a gun that shoots in random directions produce a probability distribution like those of objects or particles, but the double-slit experiment for an electron gun produce a wave-like interference pattern? I read in another thread that electrons are actually particles that are described via a wave function and that they are not actually waves. But why do they act like waves if they are not waves? If you say they have an undulatory nature, what mechanism gives them this nature and how does it determine in what scenario a particle like an electron will act like a wave?
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  3. Jan 22, 2010 #2
    I think it is not going to satisfy you, but I would like to note that what you quote as a wave is a wave in position space, but a point in momentum space. Your electrons in the double slit experiment are in a well defined state of momentum. When you detect their position on the screen, ideally they become a wave in momentum space, since you know their position at the measurement you do not know their momentum anymore. They're both, they're neither, they're quanta of the electron field.
  4. Jan 23, 2010 #3
    This may be satisfactory. Are you saying that the measurement process is what makes us perceive corpuscular or undulatory properties? Is it our ways of thinking that attributes these two properties to quanta of the electric field, via our ways of describing an experiment, and thus the physical world? Is this particle-wave duality our most accurate description of how quanta of a field behave? Is this what you mean?
  5. Jan 23, 2010 #4


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    That is pretty much the way I think about it ... to rephrase, experiments designed to measure wave properties observe the wave properties of a system, and experiments designed to measure particle properties observe the particle properties of the system. No one has figured out a way to construct an experiment that can observe both properties simultaneously.

    In the language of Dirac notation and Hilbert spaces, "a measurement is a dot-product". The way I understand this is, a quantum state is an abstract entity that we can never fully describe, but that we can conduct measurements on. We can represent both the quantum state [tex]\Psi[/tex] and the measurement [tex]\phi[/tex] as vectors in a vector space where the dimensions are a complete set of basis functions. Taking the measurement is then equivalent to taking the dot product of the dual-space analog (bra vector) of the measurement vector with the quantum state (ket vector), [tex]\left\langle\phi|\Psi\right\rangle[/tex].

    The point of all this is that by choosing the measurement, you necessarily and unavoidably restrict the set of possible outcomes, as you seemed to be saying in your post.
  6. Jan 23, 2010 #5


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    Because the de Broglie wavelengh of something as massive as a bullet is extremely small (it scales as 1/mass), but there is nothing stopping you from detecting the wave-nature of a bullet in principle
    In addition to this you have the problem of decoherence, which is more of an issue for large objects.

    Also, interference HAS been detected for very large (and massive) molecules such as C60; the only reason why the experiments are usually done with electrons is because the effects are easier to see.
  7. Jan 23, 2010 #6


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    But why would they act like "particles" when they are not particles?

  8. Jan 23, 2010 #7
    This is exactly what I am wondering. :confused:
  9. Jan 23, 2010 #8


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    Sounds like you're really asking why quantum mechanics is better at predicting the results of experiments than classical mechanics, or to put it differently, "Why is the world the way it is?". To really answer that we would need a complete theory of everything and a mathematical proof that the theory is unique.
  10. Jan 24, 2010 #9
    Hi Vectronix,

    There are several interpretations and formulations of quantum mechanics that answer your questions quite directly, but in different ways. In that regard, perhaps the most notable of such formulations is the pilot-wave theory, where the electron is described by a wavefunction and a point particle co-existing, and where the wavefunction "pilots" the motion of the point particle via an equation of motion called the guiding equation. The apparent "wave-particle duality" that you're puzzling about then has a very natural, non-paradoxical explanation in this way. This Wikipedia article gives a more detailed discussion for your interest (see section 1.1 for an account and picture of the two-slit experiment):

    Last edited: Jan 24, 2010
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